Space of modular forms of level 650, weight 2, and Character 650.d

• Label: 650.2.d
• Level: $650$
• Weight: $2$
• Character orbit: 650.d
• Rep. character: $\chi_{650}(51,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $5$
• Sturm bound: $210$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(210\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(650, [\chi])\).

	Total	New	Old
Modular forms	118	24	94
Cusp forms	94	24	70
Eisenstein series	24	0	24

Trace form

\( 24 q - 2 q^{3} - 24 q^{4} + 38 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(650, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
650.2.d.a	$650$	$2$	650.d	13.b	$2$	$2$	$2$	$5.190$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-2q^{3}-q^{4}+2iq^{6}+iq^{8}+\cdots\)
650.2.d.b	$650$	$2$	650.d	13.b	$2$	$2$	$2$	$5.190$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{3}-q^{4}+iq^{6}+3iq^{7}+\cdots\)
650.2.d.c	$650$	$2$	650.d	13.b	$2$	$6$	$6$	$5.190$	6.0.126157824.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-\beta _{3}q^{3}-q^{4}+\beta _{1}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
650.2.d.d	$650$	$2$	650.d	13.b	$2$	$6$	$6$	$5.190$	6.0.126157824.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{3}q^{3}-q^{4}-\beta _{1}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
650.2.d.e	$650$	$2$	650.d	13.b	$2$	$8$	$8$	$5.190$	8.0.303595776.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{5}q^{3}-q^{4}-\beta _{1}q^{6}+(-\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(650, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(650, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 2}\)